At 0:20, Ed is seen with a white Fender Jaguar which is incredibly similar to Johnny Marr's signature model, although the video's quality isn't great, a signature can be made out on the end of the guitar's headstock, surely meaning that Ed is playing the Johnny Marr Fender Jaguar.
Most convincingly, at 2:05, it gives a clear shot at the upper horn controls. Standard Jaguars have a switch & two rollers where as this has two switches faces different axis' from one another. Only the Johnny Marr signature model has this feature.

Posting from the Cold War Kids Instagram, Nathan Willett is holding his Fender Johnny Marr Jaguar in a supposedly rare black finish. He says:
"... Shout outs to my @fender people - for snagging this RARE black j MArr JAGuar - they only made a handful !"

While I've already submitted this as a normal Jaguar, Johnny Marr's signature can be seen on the headstock at 0:48 and I am not a moderator so I cannot change the item. Mikey's Jaguar is in the Metallic Red finish.

The 4-position blade-style pickup switch is mounted to the lower-horn chrome plate (bridge; bridge and neck in parallel; neck, bridge, and neck in series) while 2 upper-horn slide switches control pickup brightness. Other distinctive features include a Jaguar bridge with Mustang saddles and nylon bridge post inserts for improved stability; vintage-style, floating tremolo tailpiece with chrome cover; and "taller" tremolo arm with arm-sleeve nylon insert to prevent arm swing.

Marr is best known, of course, as the strikingly dynamic and influential anti-hero guitarist-arranger-allaround-musical-wunderkind behind Manchester quartet the Smiths, which virtually redefined and ruled U.K. pop throughout the 1980s. A master of melody, layering, and texture, Marr has always brought his own instantly identifiable ringing, jangling genius to the proceedings, as he has done in post-Smiths stints with The The, Electronic, the Pretenders and Johnny Marr and the Healers, and right up to the present with Modest Mouse, the Cribs and innumerable guest appearances. Includes case.

Neck Profile stunning, 4 way blade switch - genius, In-Series position, very useful! Bridge and trem are great, no sloppiness, very sensitive and controllable. This guitar cuts! but also the most versatile Jag I've come across